A “conformal + consonance” perspective/approach is attractive due to its simplicity and ability to achieve (weak and) strong prediction validity, but the addition of consonance might appear like an ad hoc adjustment or an after-thought. In Section , however, we offer a new characterization of conformal prediction, within the inferential model (IM) framework of [1]}, [2]}, in which the consonance feature is a direct consequence of the construction. Indeed, a distinguishing feature of the IM approach is its use of nested and suitably calibrated random sets for quantifying uncertainty about unobservable auxiliary variables. Since nested random sets and calibration go hand in hand with consonance and validity, respectively, this is an interesting and natural way to interpret conformal prediction. Beyond this characterization, the particular IM construction employed here—an extension of ideas in [3]}, [4]}—is, to our knowledge, the first that is not based on parametric statistical model assumptions. This nonparametric IM construction is of independent interest, and we are optimistic that the same ideas can be extended beyond prediction to the inference problem as well.
